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IOT POLY ENGINEERING

IOT POLY ENGINEERING. 3-10. January __, 2009. DRILL. With a partner, go over your solutions to last night’s homework. Make sure all work is neat and any incongruence between answers is resolved. Last night’s homework: Complete problems 4-6 on the Trig. Worksheet

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IOT POLY ENGINEERING

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  1. IOTPOLYENGINEERING 3-10 January __, 2009 DRILL • With a partner, go over your solutions to last night’s homework. Make sure all work is neat and any incongruence between answers is resolved. • Last night’s homework: • Complete problems 4-6 on the Trig. Worksheet • 2. Complete problems 1-2 on the Vector Worksheet

  2. IOTPOLYENGINEERING 3-9 N

  3. IOTPOLYENGINEERING 3-9

  4. Trigonometry and Vectors IOTPOLYENGINEERING 3-8 REVIEW Trigonometry Pythagorean Theorem: r2 = x2 + y2 B r y HYPOTENUSE A C x

  5. Trigonometry and Vectors REVIEW Common triangles in Geometry and Trigonometry 5 3 4 1

  6. Trigonometry and Vectors REVIEW Common triangles in Geometry and Trigonometry You must memorize these triangles 45o 60o 2 1 1 30o 45o 1 2 3

  7. Trigonometry and Vectors opposite hypotenuse sin A = opposite adjacent adjacent hypotenuse tan A = cos A = IOTPOLYENGINEERING 3-8 REVIEW Trigonometric Functions Trigonometric functions are ratios of the lengths of the segments that make up angles.

  8. Trigonometry and Vectors REVIEW Measuring Angles • Unless otherwise specified: • Positive angles measured counter-clockwise from the horizontal. • Negative angles measured clockwise from the horizontal. • We call the horizontal line 0o, or the initial side 90 -330 degrees -315 degrees -270 degrees -180 degrees -90 degrees 30 degrees 45 degrees 90 degrees 180 degrees 270 degrees 360 degrees = = = = = 180 0 INITIAL SIDE IOTPOLYENGINEERING 3-8 270

  9. Trigonometry and Vectors IOTPOLYENGINEERING 3-9 REVIEW Vectors • Scalar Quantities – a quantity that involves magnitude only; direction is not important • Tiger Woods – 6’1” • Shaquille O’Neill – 7’0” • Vector Quantities – a quantity that involves both magnitudeand direction How hard to impact the cue ball is only part of the game – you need to know direction too Weight is a vector quantity

  10. Trigonometry and Vectors IOTPOLYENGINEERING 3-9 REVIEW Scalar or Vector? • 400 mph due north • $100 • 10 lbs weight • 5 miles northeast • 6 yards • 1000 lbs force Magnitude and Direction Magnitude and Direction Vector Vector Magnitude only Magnitude only Scalar Scalar Magnitude and Direction Magnitude only Vector Scalar

  11. Trigonometry and Vectors IOTPOLYENGINEERING 3-9 REVIEW Vectors • Free-body Diagram • A diagram that shows all external forces acting on an object. applied force normal force N F Ff friction force force of gravity (weight) Wt

  12. Trigonometry and Vectors IOTPOLYENGINEERING 3-9 REVIEW Vectors • Describing vectors – • We MUST represent both magnitudeand direction. • Describe the force applied to the wagon by the skeleton: Hat signifies vector quantity 40 lbs 45o F = 40 lbs 45o magnitude direction

  13. Trigonometry and Vectors IOTPOLYENGINEERING 3-9 REVIEW Vectors • 2 ways of describing vectors… Students must use this form F = 40 lbs 45o F = 40 lbs @ 45o 40 lbs 45o

  14. Trigonometry and Vectors IOTPOLYENGINEERING 3-10 Vectors – Scalar Multiplication • We can multiply any vector by a whole number. • Original direction is maintained, new magnitude. 2 ½

  15. Trigonometry and Vectors IOTPOLYENGINEERING 3-10 Vectors – Addition • We can add two or more vectors together. • Redraw vectors head-to-tail, then draw the resultant vector. • (head-to-tail order does not matter)

  16. Trigonometry and Vectors IOTPOLYENGINEERING 3-10 Vectors – Rectangular Components • It is often useful to break a vector into horizontal and vertical components (rectangular components). • Consider the Force vector below. • Plot this vector on x-y axis. • Project the vector onto x and y axes. y F Fy x Fx

  17. Trigonometry and Vectors IOTPOLYENGINEERING 3-10 Vectors – Rectangular Components This means: vector F = vector Fx + vector Fy Remember the addition of vectors: y F Fy x Fx

  18. Trigonometry and Vectors IOTPOLYENGINEERING 3-10 Unit vector Vectors – Rectangular Components Vector Fx= Magnitude Fxtimes vector i F = Fx i + Fyj Fx= Fx i i denotes vector in x direction y Vector Fy= Magnitude Fytimes vector j F Fy= Fy j Fy j denotes vector in y direction x Fx

  19. Trigonometry and Vectors IOTPOLYENGINEERING 3-10 Vectors – Rectangular Components From now on, vectors on this screen will appear as bold type without hats. For example, Fx = (4 lbs)i Fy = (3 lbs)j F = (4 lbs)i + (3 lbs)j

  20. Trigonometry and Vectors IOTPOLYENGINEERING 3-10 Vectors – Rectangular Components Each grid space represents 1 lb force. What is Fx? Fx = (4 lbs)i What is Fy? Fy = (3 lbs)j What is F? F = (4 lbs)i + (3 lbs)j y F Fy x Fx

  21. Trigonometry and Vectors IOTPOLYENGINEERING 3-10 Vectors – Rectangular Components What is the relationship between Q, sin Q, and cos Q? cos Q = Fx / F Fx = F cos Qi sin Q = Fy / F Fy = F sin Qj F Fy Q Fx

  22. Trigonometry and Vectors IOTPOLYENGINEERING 3-10 Vectors – Rectangular Components When are Fx and Fy Positive/Negative? Fy + Fy + y F Fx + Fx - F x F F Fx - Fx + Fy - Fy -

  23. IOTPOLYENGINEERING 3-10 Vectors – Rectangular Components Complete the following chart in your notebook: I II III IV

  24. Rewriting vectors in terms of rectangular components: 1) Find force in x-direction – write formula and substitute 2) Find force in y-direction – write formula and substitute 3) Write as a single vector in rectangular components IOTPOLYENGINEERING Fx = F cos Qi Fy = F sin Qj

  25. IOTPOLYENGINEERING Fx = F cos Qi Fy = F sin Qj

  26. IOTPOLYENGINEERING Fx = F cos Qi Fy = F sin Qj

  27. IOTPOLYENGINEERING Fx = F cos Qi Fy = F sin Qj

  28. Trigonometry and Vectors IOTPOLYENGINEERING 3-10 Vectors – Resultant Forces Resultant forces are the overall combination of all forces acting on a body. 1) sum of forces in x-direction 2) sum of forces in y-direction 3) Write as single vector in rectangular components Fx = F cos Qi = (150 lbs) (cos 60) i = (75 lbs)i SFx= (75 lbs)i No x-component

  29. Trigonometry and Vectors IOTPOLYENGINEERING 3-10 Vectors – Resultant Forces Resultant forces are the overall combination of all forces acting on a body. 1) sum of forces in x-direction 2) sum of forces in y-direction 3) Write as single vector in rectangular components Fy = F sin Qj = (150 lbs) (sin 60) j = (75 lbs)j Wy = -(100 lbs)j SFy= (75 lbs)j - (100 lbs)j SFy = (75 - 100 lbs)j

  30. Trigonometry and Vectors IOTPOLYENGINEERING 3-10 Vectors – Resultant Forces Resultant forces are the overall combination of all forces acting on a body. 1) sum of forces in x-direction 2) sum of forces in y-direction 3) Write as single vector in rectangular components R = SFx +SFy R = (75 lbs)i + (75 - 100 lbs)j R = (75 lbs)i + (29.9 lbs)j

  31. IOTPOLYENGINEERING 3-10 Trigonometry and Vectors

  32. IOTPOLYENGINEERING 3-10 Trigonometry and Vectors

  33. IOTPOLYENGINEERING 3-10 Trigonometry and Vectors

  34. IOTPOLYENGINEERING 3-10 Trigonometry and Vectors

  35. IOTPOLYENGINEERING 3-10 Trigonometry and Vectors

  36. IOTPOLYENGINEERING 3-10 Trigonometry and Vectors

  37. IOTPOLYENGINEERING 3-10 Trigonometry and Vectors CLASSWORK/ HOMEWORK Complete problem #4 on the Vector Worksheet

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